Multiscale Modeling of Hepatitis B Virus Capsid Assembly and Its Dimorphism

Heterogeneity of HPV16 virus-like particles indicates a complex assembly energy surface

Human Papillomavirus serotype 16 (HPV16) capsid protein (L1) pentamers canonically assemble into T = 7 icosahedral capsids. Such virus-like particles are the basis of the HPV vaccine. We examined assembly of L1 pentamers in response to pH, mild oxidants, and ionic strength and found a mixture of closed, roughly spherical structures from ∼20 to ∼70 nm in diameter, indicating the presence of many kinetically accessible energy minima. Using bulk and single particle techniques we observed that the size distribution changes but does not reach homogeneity. Though heterogenous in size, particles showed uniform responses to low ionic strength dissociation, thermal unfolding, and susceptibility to protease digestion. These assays suggest maturation over time, but at different rates. Cysteine oxidation further stabilized particles at early, but not late, times without changing general characteristics including thermal stability and protease digestion. These data show complex assembly paths to species of different sizes, but with locally similar interactions.

Guanidine Hydrochloride-Induced Hepatitis B Virus Capsid Disassembly Hysteresis

Hepatitis B virus (HBV) displays remarkable self-assembly capabilities that interest the scientific community and biotechnological industries as HBV is leading to an annual mortality of up to 1 million people worldwide (especially in Africa and Southeast Asia). When the ionic strength is increased, hepatitis B virus-like particles (VLPs) can assemble from dimers of the first 149 residues of the HBV capsid protein core assembly domain (Cp149). Using solution small-angle X-ray scattering, we investigated the disassembly of the VLPs by titrating guanidine hydrochloride (GuHCl). Measurements were performed with and without 1 M NaCl, added either before or after titrating GuHCl. Fitting the scattering curves to a linear combination of atomic models of Cp149 dimer (the subunit) and T = 3 and T = 4 icosahedral capsids revealed the mass fraction of the dimer in each structure in all the titration points. Based on the mass fractions, the variation in the dimer-dimer association standard free energy was calculated as a function of added GuHCl, showing a linear relation between the interaction strength and GuHCl concentration. Using the data, we estimated the energy barriers for assembly and disassembly and the critical nucleus size for all of the assembly reactions. Extrapolating the standard free energy to [GuHCl] = 0 showed an evident hysteresis in the assembly process, manifested by differences in the dimer-dimer association standard free energy obtained for the disassembly reactions compared with the equivalent assembly reactions. Similar hysteresis was observed in the energy barriers for assembly and disassembly and the critical nucleus size. The results suggest that above 1.5 M, GuHCl disassembled the capsids by attaching to the protein and adding steric repulsion, thereby weakening the hydrophobic attraction.

Overview of the 2023 Physical Virology Gordon Research Conference-Viruses at Multiple Levels of Complexity

This review accompanies the Special Issue on the subject of physical virology, which features work presented at the recent Gordon Research Conference (GRC) on this topic [...].

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Mechanisms of allostery at the viral surface through the eyes of molecular simulation

The outermost surface layer of any virus is formed by either a capsid shell or envelope. Such layers have traditionally been thought of as immovable structures, but it is becoming apparent that they cannot be viewed exclusively as static architectures protecting the viral genome. A limited number of proteins on the virion surface must perform a multitude of functions in order to orchestrate the viral life cycle, and allostery can regulate their structures at multiple levels of organization, spanning individual molecules, protomers, large oligomeric assemblies, or entire viral surfaces. Here, we review recent contributions from the molecular simulation field to viral surface allostery, with a particular focus on the trimeric spike glycoprotein emerging from the coronavirus surface, and the icosahedral flaviviral envelope complex. As emerging viral pathogens continue to pose a global threat, an improved understanding of viral dynamics and allosteric regulation will prove crucial in developing novel therapeutic strategies.

pyCapsid: identifying dominant dynamics and quasi-rigid mechanical units in protein shells

SUMMARY

pyCapsid is a Python package developed to facilitate the characterization of the dynamics and quasi-rigid mechanical units of protein shells and other protein complexes. The package was developed in response to the rapid increase of high-resolution structures, particularly capsids of viruses, requiring multiscale biophysical analyses. Given a protein shell, pyCapsid generates the collective vibrations of its amino-acid residues, identifies quasi-rigid mechanical regions associated with the disassembly of the structure, and maps the results back to the input proteins for interpretation. pyCapsid summarizes the main results in a report that includes publication-quality figures.

AVAILABILITY AND IMPLEMENTATION

pyCapsid's source code is available under MIT License on GitHub. It is compatible with Python 3.8-3.10 and has been deployed in two leading Python package-management systems, PIP and Conda. Installation instructions and tutorials are available in the online documentation and in the pyCapsid's YouTube playlist. In addition, a cloud-based implementation of pyCapsid is available as a Google Colab notebook. pyCapsid Colab does not require installation and generates the same report and outputs as the installable version. Users can post issues regarding pyCapsid in the repository's issues section.

Insight into structural biophysics from solution X-ray scattering

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement.

Structure of the Hepatitis B virus capsid quasi-6-fold with a trapped C-terminal domain reveals capsid movements associated with domain exit

Many viruses undergo transient conformational change to surveil their environments for receptors and host factors. In Hepatitis B virus (HBV) infection, after the virus enters the cell, it is transported to the nucleus by interaction of the HBV capsid with an importin α/β complex. The interaction between virus and importins is mediated by nuclear localization signals on the capsid protein's C-terminal domain (CTD). However, CTDs are located inside the capsid. In this study, we asked where does a CTD exit the capsid, are all quasi-equivalent CTDs created equal, and does the capsid structure deform to facilitate CTD egress from the capsid? Here, we used Impβ as a tool to trap transiently exposed CTDs and examined this complex by cryo-electron microscopy. We examined an asymmetric reconstruction of a T = 4 icosahedral capsid and a focused reconstruction of a quasi-6-fold vertex (3.8 and 4.0 Å resolution, respectively). Both approaches showed that a subset of CTDs extended through a pore in the center of the quasi-6-fold complex. CTD egress was accompanied by enlargement of the pore and subtle changes in quaternary and tertiary structure of the quasi-6-fold. When compared to molecular dynamics simulations, structural changes were within the normal range of capsid flexibility. Although pore diameter was enlarged in the Impβ-bound reconstruction, simulations indicate that CTD egress does not exclusively depend on enlarged pores. In summary, we find that HBV surveillance of its environment by transient exposure of its CTD requires only modest conformational change of the capsid.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

Molecular Dynamics Simulations of Deformable Viral Capsomers

Most coarse-grained models of individual capsomers associated with viruses employ rigid building blocks that do not exhibit shape adaptation during self-assembly. We develop a coarse-grained general model of viral capsomers that incorporates their stretching and bending energies while retaining many features of the rigid-body models, including an overall trapezoidal shape with attractive interaction sites embedded in the lateral walls to favor icosahedral capsid assembly. Molecular dynamics simulations of deformable capsomers reproduce the rich self-assembly behavior associated with a general T=1 icosahedral virus system in the absence of a genome. Transitions from non-assembled configurations to icosahedral capsids to kinetically-trapped malformed structures are observed as the steric attraction between capsomers is increased. An assembly diagram in the space of capsomer-capsomer steric attraction and capsomer deformability reveals that assembling capsomers of higher deformability into capsids requires increasingly large steric attraction between capsomers. Increasing capsomer deformability can reverse incorrect capsomer-capsomer binding, facilitating transitions from malformed structures to symmetric capsids; however, making capsomers too soft inhibits assembly and yields fluid-like structures.

Structure of the HIV immature lattice allows for essential lattice remodeling within budded virions

For HIV virions to become infectious, the immature lattice of Gag polyproteins attached to the virion membrane must be cleaved. Cleavage cannot initiate without the protease formed by the homo-dimerization of domains linked to Gag. However, only 5% of the Gag polyproteins, termed Gag-Pol, carry this protease domain, and they are embedded within the structured lattice. The mechanism of Gag-Pol dimerization is unknown. Here, we use spatial stochastic computer simulations of the immature Gag lattice as derived from experimental structures, showing that dynamics of the lattice on the membrane is unavoidable due to the missing 1/3 of the spherical protein coat. These dynamics allow for Gag-Pol molecules carrying the protease domains to detach and reattach at new places within the lattice. Surprisingly, dimerization timescales of minutes or less are achievable for realistic binding energies and rates despite retaining most of the large-scale lattice structure. We derive a formula allowing extrapolation of timescales as a function of interaction free energy and binding rate, thus predicting how additional stabilization of the lattice would impact dimerization times. We further show that during assembly, dimerization of Gag-Pol is highly likely and therefore must be actively suppressed to prevent early activation. By direct comparison to recent biochemical measurements within budded virions, we find that only moderately stable hexamer contacts (-12kBT<∆G<-8kBT) retain both the dynamics and lattice structures that are consistent with experiment. These dynamics are likely essential for proper maturation, and our models quantify and predict lattice dynamics and protease dimerization timescales that define a key step in understanding formation of infectious viruses.

Understanding Virus Structure and Dynamics through Molecular Simulations

Viral outbreaks remain a serious threat to human and animal populations and motivate the continued development of antiviral drugs and vaccines, which in turn benefits from a detailed understanding of both viral structure and dynamics. While great strides have been made in characterizing these systems experimentally, molecular simulations have proven to be an essential, complementary approach. In this work, we review the contributions of molecular simulations to the understanding of viral structure, functional dynamics, and processes related to the viral life cycle. Approaches ranging from coarse-grained to all-atom representations are discussed, including current efforts at modeling complete viral systems. Overall, this review demonstrates that computational virology plays an essential role in understanding these systems.

Self-assembly coupled to liquid-liquid phase separation

Liquid condensate droplets with distinct compositions of proteins and nucleic acids are widespread in biological cells. While it is known that such droplets, or compartments, can regulate irreversible protein aggregation, their effect on reversible self-assembly remains largely unexplored. In this article, we use kinetic theory and solution thermodynamics to investigate the effect of liquid-liquid phase separation on the reversible self-assembly of structures with well-defined sizes and architectures. We find that, when assembling subunits preferentially partition into liquid compartments, robustness against kinetic traps and maximum achievable assembly rates can be significantly increased. In particular, both the range of solution conditions leading to productive assembly and the corresponding assembly rates can increase by orders of magnitude. We analyze the rate equation predictions using simple scaling estimates to identify effects of liquid-liquid phase separation as a function of relevant control parameters. These results may elucidate self-assembly processes that underlie normal cellular functions or pathogenesis, and suggest strategies for designing efficient bottom-up assembly for nanomaterials applications.

Long-time scale simulations of virus-like particles from three human-norovirus strains

The dynamics of the virus like particles (VLPs) corresponding to the GII.4 Houston, GII.2 SMV, and GI.1 Norwalk strains of human noroviruses (HuNoV) that cause gastroenteritis was investigated by means of long-time (about 30 μs in the laboratory timescale) molecular dynamics simulations with the coarse-grained UNRES force field. The main motion of VLP units turned out to be the bending at the junction between the P1 subdomain (that sits in the VLP shell) and the P2 subdomain (that protrudes outside) of the major VP1 protein, this resulting in a correlated wagging motion of the P2 subdomains with respect to the VLP surface. The fluctuations of the P2 subdomain were found to be more pronounced and the P2 domain made a greater angle with the normal to the VLP surface for the GII.2 strain, which could explain the inability of this strain to bind the histo-blood group antigens (HBGAs).

Engineering Metastability into a Virus-like Particle to Enable Triggered Dissociation

For a virus-like particle (VLP) to serve as a delivery platform, the VLP must be able to release its cargo in response to a trigger. Here, we use a chemical biology approach to destabilize a self-assembling capsid for a subsequent triggered disassembly. We redesigned the dimeric hepatitis B virus (HBV) capsid protein (Cp) with two differentially addressable cysteines, C150 for reversibly crosslinking the capsid and C124 to react with a destabilizing moiety. The resulting construct, Cp150-V124C, assembles into icosahedral, 120-dimer VLPs that spontaneously crosslink via the C-terminal C150, leaving C124 buried at a dimer-dimer interface. The VLP is driven into a metastable state when C124 is reacted with the bulky fluorophore, maleimidyl BoDIPY-FL. The resulting VLP is stable until exposed to modest, physiologically relevant concentrations of reducing agent. We observe dissociation with FRET relaxation of polarization, size exclusion chromatography, and resistive-pulse sensing. Dissociation is slow, minutes to hours, with a characteristic lag phase. Mathematical modeling based on the presence of a nucleation step predicts disassembly dynamics that are consistent with experimental observations. VLPs transfected into hepatoma cells show similar dissociation behavior. These results suggest a generalizable strategy for designing a VLP that can release its contents in an environmentally responsive reaction.

Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China

Hepatitis B virus (HBV) infection is a global public health problem and there are 257 million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.